Conic sections

Question 1

What are the four types of conic sections?

Answer 1

Circle, ellipse, parabola, hyperbola.

Question 2

True or False: A circle is a type of ellipse.

Answer 2

True.

Question 3

Fill in the blank: A parabola opens either _____ or _____.

Answer 3

upward, downward.

Question 4

What is the standard form equation of a circle with center (h, k) and radius r?

Answer 4

(x - h)² + (y - k)² = r².

Question 5

What is the general form of the equation of an ellipse?

Answer 5

(x²/a²) + (y²/b²) = 1.

Question 6

Identify the conic section: x² + y² - 4x - 6y + 9 = 0.

Answer 6

Circle.

Question 7

What is the definition of a hyperbola?

Answer 7

A set of points where the difference of the distances to two foci is constant.

Question 8

True or False: The foci of a hyperbola are located along the transverse axis.

Answer 8

True.

Question 9

What is the equation of a horizontal hyperbola?

Answer 9

(x²/a²) - (y²/b²) = 1.

Question 10

Short answer: What is the directrix of a parabola?

Answer 10

A fixed line used in the definition of a parabola.

Question 11

Fill in the blank: The major axis of an ellipse is the longest diameter that passes through the _____ and _____.

Answer 11

foci, center.

Question 12

What is the eccentricity of a circle?

Answer 12

0.

Question 13

Identify the conic section described: A set of all points in a plane equidistant from a point and a line.

Answer 13

Parabola.

Question 14

What is the standard form of the equation for a vertical ellipse?

Answer 14

(x²/b²) + (y²/a²) = 1.

Question 15

True or False: The vertices of a hyperbola are located at the endpoints of the conjugate axis.

Answer 15

False.

Question 16

What do the terms ‘focus’ and ‘directrix’ relate to in conic sections?

Answer 16

They define the shape of conics, particularly parabolas.

Question 17

What is the difference between a major axis and a minor axis in an ellipse?

Answer 17

The major axis is longer than the minor axis.

Question 18

Fill in the blank: The distance between the foci of a hyperbola is _____ than the distance between the vertices.

Answer 18

greater.

Question 19

What is the standard form of a parabola that opens to the right?

Answer 19

(y - k)² = 4p(x - h).

Question 20

Identify the conic section: x² - 4y² = 16.

Answer 20

Hyperbola.

Question 21

What is the formula for eccentricity (e) of an ellipse?

Answer 21

e = c/a, where c is the distance from the center to a focus.

Question 22

True or False: All conic sections can be represented by second-degree polynomial equations.

Answer 22

True.

Question 23

What does the term ‘latus rectum’ refer to in a parabola?

Answer 23

The line segment perpendicular to the axis of symmetry, passing through the focus.

Question 24

Fill in the blank: The foci of an ellipse are located _____ the center.

Answer 24

inside.

Question 25

What is the relationship between the axes of symmetry in a hyperbola?

Answer 25

They are perpendicular to each other.

Question 26

Identify the conic section: 9x² + 16y² = 144.

Answer 26

Ellipse.

Question 27

What is the equation of a vertical hyperbola?

Answer 27

(y²/a²) - (x²/b²) = 1.

Question 28

True or False: The vertices of a parabola are located at the focus.

Answer 28

False.

Question 29

Fill in the blank: The center of a hyperbola is the midpoint between the _____ and _____.

Answer 29

foci, vertices.

Question 30

What is the standard form of the equation for an ellipse with a vertical major axis?

Answer 30

(y - k)²/a² + (x - h)²/b² = 1.